Question

The sum of three consecutive multiples of 11 is 363. Find multiples of 11.

Answer 1

Hint: We will consider the consecutive numbers of 11 and form the required question. After this we will solve for the variable in the same equation. After this we will again substitute the value of the variable into the three supposed consecutive numbers. By applying the steps we will be able to solve the question further.

Complete step-by-step answer:
According to the question we have three multiples of 11. So, we will consider the numbers as 11x, 11y and 11z as in consecutive form.
We have been given the sum of the numbers is 363. This results in 11x + 11y + 11z = 363.
Now we will substitute y as x + 1 to make it a just next number of x. Similarly, we will put z as x + 2 as the next to next number of x. Therefore, the equation changes into 11x + 11(x +1) + 11(x + 2) = 363.
Therefore, we get 11x + 11x + 11 + 11x + 22 = 363. Thus we get 33x + 33 = 363.
Now we will take 33 to the right side of the equation. Thus we will get 33x = 363 – 33.
After solving this equation we get that 33x = 330.
Now, we will divide this equation by 33. Therefore, we will get x = 10.
We will now consider 11x, 11y and 11z as in consecutive form. As we know that y = x + 1 and z = x + 2 thus we get 11x, 11(x +1) and 11(x+2) as in consecutive form.
After we are going to substitute the values of x in these three terms we get 11(10), 11(10 + 1) and 11(10 + 2).
Thus, we get the numbers as 110, 11(11) and 11(12) or we can also write these as 110, 121 and 132.
Hence, the required multiples of 11 are 110, 121 and 132.

Note: It should be noted here that the question is talking about the consecutive multiples of 11 and not consecutive numbers. That is why we got three consecutive multiples of 11 which are x = 10, x + 1 = 11 and x = 12. We will take care of the fact that any number that is taken to the either side of the equation will have a sign change. For example in the equation 33x + 33 = 363 we took 33 to the right side of the equation. Along with that we have changed its sign from + to – sign. By considering these points we will be able to answer the question correctly otherwise we will get it wrong.